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Mathematics

In the following table, do x and y vary directly:

xy
1632
3060
4080
5684

Direct & Inverse Variations

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Answer

x1y1=1632=12,x2y2=3060=12,x3y3=4080=12,x4y4=5684=23,\dfrac{x1}{y1} = \dfrac{16}{32} = \dfrac{1}{2},\\[1em] \dfrac{x2}{y2} = \dfrac{30}{60} = \dfrac{1}{2},\\[1em] \dfrac{x3}{y3} = \dfrac{40}{80} = \dfrac{1}{2},\\[1em] \dfrac{x4}{y4} = \dfrac{56}{84} = \dfrac{2}{3},\\[1em]

x1y1=x2y2=x3y3x4y4\Rightarrow \dfrac{x1}{y1} = \dfrac{x2}{y2} = \dfrac{x3}{y3} ≠ \dfrac{x4}{y4} = not a constant

Hence, x and y are not in direct variation.

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